US11907331B1ActiveUtilityPatentIndex 69
Method and system for evaluating fractal dimension of particle matter in dispersing system
Est. expiryMar 27, 2043(~16.7 yrs left)· nominal 20-yr term from priority
G06F 17/18G06T 5/002G06T 5/20G06T 2207/10056G06T 2207/20032G06T 5/70G06T 7/62G06T 2207/20112G06T 2207/30242
69
PatentIndex Score
2
Cited by
8
References
10
Claims
Abstract
Disclosed in the present invention are a method and system for evaluating a fractal dimension of particle matter in a dispersing system. The method includes: setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ 2 ) with an expectation μ and a standard deviation σ, and determining the value of the standard deviation σ; and evaluating a fractal dimension D ƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being: D ƒ =1/σ. The present invention provides the formula for evaluating the fractal dimension of particle distribution in a dispersing system. When the formula is used to calculate a fractal dimension, only particle radius distribution of particle matter needs to be measured, and no geometrical morphology feature parameter of the particle matter needs to be measured. Factors such as particle morphology and the like do not affect the fractal dimension. Therefore, the measurement method of the present invention can reduce an error resulting from experimental measurements, can acquire a fractal dimension of particle matter quickly and efficiently, and is especially adapted to data analysis of a dispersion system and a particle swarm.
Claims
exact text as granted — not AI-modifiedThe invention claimed is:
1. A method for evaluating a fractal dimension of particle matter in a dispersing system, the method comprising:
setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ 2 ) with an expectation μ and a standard deviation σ, acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution; and
evaluating the fractal dimension D ƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being:
D
f
=
1
σ
.
2. The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 1 , wherein the acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution comprises:
particle radius distribution determination: determining the particle radius r i of the particle matter in the dispersing system and a particle content p i of the particle matter having the particle radius r i ; and
fitting: fitting particle radius distribution of the particle matter in the dispersing system by using a standard logarithmic normal distribution function, so as to determine an expectation μ and a standard deviation σ in the logarithmic normal distribution function, the form of the logarithmic normal distribution function being:
f
(
r
)
=
1
r
2
π
σ
e
-
(
l
n
r
-
ln
μ
)
2
2
σ
2
wherein, ƒ(r) is a distribution probability density function of the particle radius r.
3. The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2 , wherein the particle radius distribution determination is implemented by using a laser particle sizer.
4. The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2 , wherein the particle radius distribution determination is implemented on the basis of computer image recognition, comprising:
step S 110 , acquiring a microscopic image by means of a microscopic image capture card;
step S 120 , removing background or environmental noise by means of median filtering;
step S 130 , reprocessing the image by means of 0-1 integer optimization;
step S 140 , marking a connected domain of a particle and the position of a central point thereof according to a seed fill algorithm in the graph theory; and
step S 150 , calculating the particle radius of the marked particle on the basis of the equivalence principle, and storing the same in a data structure, wherein the equivalence principle refers to using the area of the marked connected domain as the area of a circle, and calculating the radius as an equivalent radius of the corresponding particle, and the particle radius r i of the particle matter and the particle content p i of the particle matter having the particle radius r i are acquired according to stored data of the data structure.
5. The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2 , wherein the fitting comprises:
dividing the particle radii into several ranges, counting the number of particles in each range, drawing a particle size distribution diagram, and performing polynomial fitting and optimization on a particle size distribution curve by using a least square method, to acquire the logarithmic normal distribution function of the particle radius distribution.
6. The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 1 , wherein the acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution comprises:
particle radius distribution determination: determining the particle radius r i of the particle matter in the dispersing system and a particle content p i of the particle matter having the particle radius r i ;
first calculation: calculating an expectation E(r) and a variance D(r) of particle radius distribution of the particle matter in the dispersing system, calculation formulas being:
E
(
r
)
=
∑
i
=
1
n
r
i
p
i
D
(
r
)
=
∑
i
=
1
n
[
r
i
-
E
(
r
)
]
2
p
i
and second calculation: calculating the standard deviation σ of the particle radius distribution of the particle matter on the basis of the calculated expectation E(r) and variance D(r), a calculation formula being:
σ
=
ln
[
1
+
D
(
r
)
E
(
r
)
2
]
wherein, n is the number of particle radii of the particle matter.
7. A system for evaluating a fractal dimension of particle matter in a dispersing system, characterized by comprising:
a distribution parameter calculation module, for acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution, setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ 2 ) with an expectation μ and a standard deviation σ; and
a fractal dimension calculation module, for evaluating the fractal dimension D ƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being:
D
f
=
1
σ
.
8. The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 7 , wherein the distribution parameter calculation module comprises:
a particle radius distribution determination unit, for determining the particle radius r i of the particle matter in the dispersing system and a particle content p i of the particle matter having the particle radius r i ; and
a fitting unit, for fitting particle radius distribution of the particle matter in the dispersing system by using a standard logarithmic normal distribution function, so as to determine an expectation μ and a standard deviation σ in the logarithmic normal distribution function, the form of the logarithmic normal distribution function being:
f
(
r
)
=
1
r
2
π
σ
e
-
(
l
n
r
-
ln
μ
)
2
2
σ
2
wherein, ƒ(r) is a distribution probability density function of the particle radius r.
9. The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 8 , wherein the particle radius distribution determination unit comprises:
a filtering subunit, for performing median filtering on a microscopic image acquired by means of a microscopic image capture card, so as to remove background or environmental noise;
an integer optimization subunit, for reprocessing the filtered image by means of 0-1 integer optimization;
a marking subunit, for marking a connected domain of a particle and the position of a central point thereof according to a seed fill algorithm in the graph theory; and
an equivalent radius calculation subunit, for calculating the particle radius of the marked particle on the basis of the equivalence principle, and storing the same in a data structure, wherein the equivalence principle refers to using the area of the marked connected domain as the area of a circle, and calculating the radius as an equivalent radius of the corresponding particle.
10. The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 7 , wherein the distribution parameter calculation module comprises:
a particle radius distribution determination unit, for determining the particle radius r i of the particle matter in the dispersing system and a particle content p i of the particle matter having the particle radius r i ;
a first calculation unit, for calculating an expectation E(r) and a variance D(r) of particle radius distribution of the particle matter in the dispersing system, calculation formulas being:
E
(
r
)
=
∑
i
=
1
n
r
i
p
i
D
(
r
)
=
∑
i
=
1
n
[
r
i
-
E
(
r
)
]
2
p
i
and a second calculation unit, for calculating the standard deviation σ of the particle radius distribution of the particle matter on the basis of the calculated expectation E(r) and variance D(r), a calculation formula being:
σ
=
ln
[
1
+
D
(
r
)
E
(
r
)
2
]
wherein, n is the number of particle radii of the particle matter.Cited by (0)
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